Journal article icon

Journal article

Exactness of quadrature formulas

Abstract:

The standard design principle for quadrature formulas is that they should be exact for integrands of a given class, such as polynomials of a fixed degree. We review the subject from this point of view and show that this principle fails to predict the actual behavior in four of the best-known cases: Newton–Cotes, Clenshaw–Curtis, Gauss–Legendre, and Gauss–Hermite quadrature. New results include (i) the observation that $x^k$ is integrated accurately by the Newton–Cotes formula even though the ...

Expand abstract
Publication status:
Published
Peer review status:
Peer reviewed

Actions


Access Document


Files:
Publisher copy:
10.1137/20M1389522

Authors


More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Balliol College
Role:
Author
ORCID:
0000-0003-2504-1709
Publisher:
Society for Industrial and Applied Mathematics
Journal:
SIAM Review More from this journal
Volume:
64
Issue:
1
Pages:
132–150
Publication date:
2022-02-03
Acceptance date:
2021-06-07
DOI:
EISSN:
1095-7200
ISSN:
0036-1445
Language:
English
Keywords:
Pubs id:
1159260
Local pid:
pubs:1159260
Deposit date:
2021-07-24

Terms of use


Views and Downloads






If you are the owner of this record, you can report an update to it here: Report update to this record

TO TOP